1. Lesson Two The Index of Refraction & Total Internal Reflection
Chapter 11
Lesson Two
The Index of Refraction
&
Total Internal Reflection

2. Learning Goal
To apply our understanding of refraction to light rays traveling through different mediums
To calculate the index of refraction for various substances
To learn about how total internal reflection occurs

3. Introduction
French physicist Jean Foucault made the first measurement of the speed of light in a medium (other than a vacuum or air), in 1862.
He measured the speed of light in water to be 2.25 × 10 8 m/s.
Since then, the speed of light has been measured for a variety of media

4. Introduction

5. Introduction The speed of light is different for each medium
BUT is ALWAYS LESS than the speed of light in a vacuum (~ 3.00 x 108 m/s)
The change in the speed of light at the boundary of a substance causes refraction.
The speed of light in a medium is a distinctive optical property of that medium

6. Index of Refraction
The index of refraction for a medium is defined as:
the ratio of the speed of light in a vacuum to the speed of light in that medium.
Mathematically, the index of refraction is written as
where n is the index of refraction
c is the speed of light in a vacuum (3.0 x 108 m/s)
v is the speed of light in a given medium

7. Index of Refraction

8. Index of Refraction
Since the index of refraction is calculated based on light traveling through different mediums in comparison to light traveling through a vacuum
We need to know the following variables for such mediums

9. Optical Density and Light Speed
After looking at the index of refraction, a relationship can be seen when looking at the density of various mediums compared to their index of refraction values
Optical density of a material looks at atoms of a material that maintain absorbed energy of an electromagnetic wave
Where, the more optically dense that a material is, the slower that a wave will move through the material.

10. Optical Density and Light Speed
Thus we can relate optical density to the index of refraction, where:
As the Index of refraction value increases
The optical density increases
The speed of light in that material decreases
Closer to the Normal the refracted ray will be found

11. Optical Density and Light Speed
Air to Glass
 Index of refraction value (air: 1.0 vs. glass: 1.52)
 Optical density (glass is more dense than air)
 Speed of light as it travels from air into glass
Refracted ray of light going through the glass will be closer to the normal (34.5° vs 60 °)

12. Optical Density and Light Speed
Air to Water
 Index of refraction value (air: 1.0 vs. water: 1.33)
 Optical density (water is more dense than air)
 Speed of light as it travels from air into water
Refracted ray of light going through the glass will be closer to the normal (40.6° vs 60 °)

13. Calculating Index of Refraction

14. Calculating Index of Refraction
You have just seen how the formula n = c ÷ v can be used to determine the index of refraction, n, for a medium
The same formula can also be used to calculate the speed at which light travels in that medium (v)
Where:
4 (n) = 3 ( c ) / 12 (v) c n v

15. Calculating Index of Refraction

16. Checking for Understanding

17. Answer Key

18. Total Internal Reflection

19. Introduction
When light travels from one medium into another, some of the light is reflected and some is refracted.
We know that light slows down when it travels from air into a denser medium like acrylic or water
This results in the light bending toward the normal
See the angle is smaller

20. Introduction
Light, however, bends away from the normal when it speeds up at the boundary of two media
Just like when light travels from acrylic into air
Where - the angle of refraction is always larger than the angle of incidence

21. Introduction Eventually, the angle of refraction will become 90°
In fact, the angle of refraction continues to increase as the angle of incidence increases
Eventually, the angle of refraction will become 90°
The angle of incidence at this point is called the critical angle
The critical angle is the angle of incidence that produces a refracted angle of 90°

22. Critical Angle

23. Critical Angle

24. Total Internal Reflection
If you increase the angle of incidence past the critical angle, the refracted ray will no longer exit the medium.
Instead, it will reflect back into the medium.
In other words, the refracted ray disappears
Where only a reflected ray is total internal reflection the situation visible
This phenomenon is called total internal reflection

25. Total Internal Reflection

26. Total Internal Reflection
Total internal reflection occurs when these two conditions are met:
Light is travelling more slowly in the first medium than in the second
The angle of incidence is large enough that no refraction occurs in the second medium. Instead, the ray is reflected back into the first medium

27. Total Internal Reflection

28. Diamonds Are Forever
One of the features that make diamonds so attractive in jewellery is the fact that they sparkle
This “sparkling” is due to the cut of the diamond faces, combined with the high index of refraction for diamond (n = 2.42) results in the total internal reflection of light.

29. Diamonds Are Forever
The high refractive index means that diamonds have a very small critical angle: 24.4°
So a lot of incident light undergoes total internal reflection inside the diamond
A light ray can bounce around several times inside the diamond before eventually exiting through a top face of the gemstone = sparkle

30. Diamonds Are Forever

31. ~ Fibre Optics ~
Fibre optics is a technology that uses light to transmit information along a glass cable.
In order for this to work, the light doesn’t escape as it travels along the cable
This is done using small critical angles inside the cable so that light entering it will have an angle of incidence greater than the critical angle

32. ~ Fibre Optics ~
Substances that have a small critical angle include high-purity glass & special types of plastics, like Lucite
Optical devices like periscopes, binoculars, and fibre optic cables make use of total internal reflection

33. The Triangular Prism
A triangular prism also exhibits total internal reflection
The critical angle for glass is about 41.1°
If a prism is oriented in such a way that the angle of incidence is greater than 41.1°, total internal reflection will result
Prisms are much more useful to reflect light than mirrors because a prism reflects almost 100 % of the light internally

34. The Triangular Prism
Depending on how you position a triangular prism, you can change the direction of light:
At 90° so that you see one total internal reflection or
At 180° and see two total internal reflections

35. Checking for Understanding